Anisotropic Reversible Aggregation of Latex Nanoparticles Suspended in a Lyotropic Nematic Liquid Crystal: Effect of Gradients of Biaxial Order

We studied the anisotropic aggregation of spherical latex particles dispersed in a lyotropic liquid crystal presenting three nematic phases; calamitic, biaxial, and discotic. We observed that in the nematic calamitic phase aggregates of latex particles are formed, which become larger and anisotropic in the vicinity of the transition to the discotic phase, due to a coalescence process. Such aggregates are weakly anisotropic and up to 50 mu m long and tend to align parallel to the director field. At the transition to the discotic phase, the aggregates dissociated and re-formed when the system was brought back to the calamitic phase. This shows that the aggregation is due to attractive and repulsive forces generated by the particular structure of the nematic phase. The surface-induced positional order was investigated by surface force apparatus experiments with the lyotropic system confined between mica surfaces, revealing the existence of a presmectic wetting layer around the surfaces and oscillating forces of increasing amplitude as the confinement thickness was decreased. We discuss the possible mechanisms responsible for the reversible aggregation of latex particles, and we propose that capillary condensation of the N(C) phase, induced by the confinement between the particles, could reduce or remove the gradient of order parameter, driving the transition of aggregates from solidlike to liquidlike and gaslike.

Conjugated equine estrogen, raloxifene and arterial stiffness in postmenopausal women

Methods We analyzed the influence of conjugated equine estrogen (CEE) and raloxifene on arterial stiffness. Sixty-seven healthy, normotensive women 1-10 years into menopause were assigned to receive oral placebo, conjugated equine estrogen 0.625mg, or raloxifene 60mg. Arterial stiffness was evaluated by measuring the carotid-femoral and femoral-dorsalis pedis pulse wave velocity (CF PWV, FP PWV). Systolic pressure augmentation index (AI) at the carotid artery was obtained with applanation tonometry. Results Arterial stiffness was not affected by any treatment regimen: placebo (CF PWV before vs. after: 644 vs. 626 cm/s, p = 0.09; FP PWV before vs. after: 1006 vs. 1012 cm/s, p = 0.77; AI before vs. after = 30 vs. 29%, p = 0.55), CEE (CF PWV before vs. after: 642 vs. 600 cm/s, p = 0.11; FP PWV before vs. after: 952 vs. 971 cm/s, p = 0.66; AI before vs. after: 25 vs. 32%, p = 0.82), and raloxifene (CF PWV before vs. after: 636 vs. 601 cm/s, p = 0.12; FP PWV before vs. after: 964 vs. 941 cm/s, p = 0.62; AI before vs. after: 25 vs. 25%, p = 0.65). A correlation occurred between basal stiffness and the degree of reduction in indexes measured, indicating that the higher the basal stiffness, the greater the degree of reduction, particularly in the CEE group: CF PWV (r = -0.602, p = 0.001); FP PWV (r = -0.455, p = 0.022); AI (r = -0.410, p = 0.042). Conclusions Conjugated equine estrogen and raloxifene do not seem to affect arterial stiffness of healthy normotensive women less than 10 years since menopause. Reduction in arterial stiffness seems related to its basal level.

Diabetes induces metabolic alterations in dental pulp

Diabetes can interfere in tissue nutrition and can impair dental pulp metabolism. This disease causes oxidative stress in cells and tissues. However, little is known about the antioxidant system in the dental pulp of diabetics. Thus, it would be of importance to study this system in this tissue in order to verify possible alterations indicative of oxidative stress. The aim of this study was to evaluate some parameters of antioxidant system of the dental pulp of healthy (n = 8) and diabetic rats (n = 8). Diabetes was induced by streptozotocin in rats. Six weeks after diabetes induction, a pool of the dental pulp of the 4 incisors of each rat (healthy and diabetic) was used for the determination of total protein and sialic acid concentrations and catalase and peroxidase activities. Data were compared by a Student t test (p <= 0.05). Dental pulps from both groups presented similar total protein concentrations and peroxidase activity. Dental pulps of diabetic rats exhibited significantly lower free, conjugated, and total sialic acid concentrations than those of control tissues. Catalase activity in diabetic dental pulps was significantly enhanced in comparison with that of control pulps. The result of the present study is indicative of oxidative stress in the dental pulp caused by diabetes. The increase of catalase activity and the reduction of sialic acid could be resultant of reactive oxygen species production.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.